Question 391047
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You cannot determine the consecutive integer values of *[tex \Large x] between which each real zero is located because the zeros are all integers in the first place.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^3\ +\ 3x^2\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\left(x\ +\ 3\right)\ =\ 0]


Hence, *[tex \Large x\ =\ 0], *[tex \Large x\ =\ 0], or *[tex \Large x\ =\ -3]


Relative maximum appears to be at *[tex \Large x\ =\ -2] and relative minimum appears to be at *[tex \Large x\ =\ 0]


Check:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\ \left(x^3\ +\ 3x^2\right)\ =\ 3x^2\ +\ 6x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ +\ 6x\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 0]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -2]


Hence extrema at *[tex \Large x\ =\ 0] or *[tex \Large x\ =\ -2]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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